Pith Number

pith:ZVQU7TR4

pith:2012:ZVQU7TR4NEB3XFG4FXPOZ5OYFR

not attested not anchored not stored refs pending

The Brill-Noether rank of a tropical curve

Yoav Len

arxiv:1209.6309 v2 · 2012-09-27 · math.AG · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZVQU7TR4NEB3XFG4FXPOZ5OYFR}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T02:55:11.542333Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cd614fce3c6903bb94dc2ddeecf5d82c5923a10c6b0cb4d023e07f2c263c5384

Aliases

arxiv: 1209.6309 · arxiv_version: 1209.6309v2 · doi: 10.48550/arxiv.1209.6309 · pith_short_12: ZVQU7TR4NEB3 · pith_short_16: ZVQU7TR4NEB3XFG4 · pith_short_8: ZVQU7TR4

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ZVQU7TR4NEB3XFG4FXPOZ5OYFR \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: cd614fce3c6903bb94dc2ddeecf5d82c5923a10c6b0cb4d023e07f2c263c5384

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1e3c28b80b779dd51d47377d701fba11a60523ed00defa303ac1e7638d0ab4ee",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-09-27T18:00:49Z",
    "title_canon_sha256": "1e420171d014800406757120f9ff3463045348d1df70d0a44e16bf809e01d77b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.6309",
    "kind": "arxiv",
    "version": 2
  }
}